Scanner for probe microscopy

ABSTRACT

A scanner for probe microscopy that avoids low resonance frequencies and accounts better for piezo nonlinearities. The x, y and z axes of a linear stack scanner are partially decoupled from each other while maintaining all mechanical joints stiff in the direction of actuation. The scanning probe microscope comprises a probe, a housing, at least two actuators, each coupled to the housing, and a support coupled to the housing and to at least a first of the actuators at a position spaced from the point at which the actuator is coupled to the housing. The support constrains the motion of the first actuator along a first axis while permitting translation along a second axis. The actuators are preferably orthogonally arranged linear stacks of flat piezos, preferably in push-pull configuration. The support can take different forms in different embodiments of the invention. In a particular embodiment, the scanner is a 2D scanner having a support frame with x and y axes, and a member for supporting an object to be moved such as a sample for a probe, the scanner comprising a flexure and flexure coupled cross-conformed piezos arranged along x and y axes. Expansion of the piezos is measured by at least two strain gauges disposed to measure the differential motion of at least two opposed actuators. The strain gauges are preferably arranged to compensate for ambient temperature changes, and preferably two or more strain gauges of identical type are disposed on each actuator to magnify the strain signal.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

This invention was made with Government support under Grant No.NSF-DMR9988640 AND NSF-DMR0080034 awarded by the National ScienceFoundation and by the National Institutes of Health under Award No.NCC-1-02037. The Government has certain rights in this invention.

FIELD OF THE INVENTION

This invention relates to the field of scanning probe devices. Moreparticularly, the invention relates to improvements in an atomic forcemicroscope used to measure the deflections of a cantilever.

BACKGROUND OF THE INVENTION

Scanning probe devices, such as the atomic force microscope (“AFM”) haveproven to be excellent tools for imaging a wide range of materials suchas metals, semiconductors, minerals, polymers, and biomaterials. In anAFM, forces are measured by means of a cantilever that deflects whenforces act on it. The deflection of the cantilever is sensed by adetection system, commonly by focusing an incident beam as a spot ontothe cantilever and directing the reflected beam onto a segmenteddetector. Specialized AFMs called “force pullers” have been built forthe purpose of pulling on molecules to determine the structure anddynamics of those molecules.

Since its introduction, the AFM and its cantilever sensor have becomeincreasingly more advanced, measuring decreasingly smaller forces andutilizing decreasingly smaller cantilevers. This has introduced problemsrelating to the sensitivity of the instrument. There is a need toprovide greater sensitivity to accommodate the smaller cantilevers andsmaller forces that scientific investigators need to either measuresamples or manipulate them. Similar detection techniques are also usedto monitor the motion of the optical probes used in near-field scanningoptical microscopes, scanning ion-conductance microscopes, and a varietyof other scanning probe microscopes. The growing field of nanotechnologyalso provides ample motivation for the precision measurement of theposition and/or motion of a wide variety of objects down to thenanometer scale and below.

The development of new small cantilevers with resonance frequencies twoorders of magnitude higher than conventional cantilevers make thedetection mechanism and the cantilever response much faster thannecessary for conventional AFM systems. The speed of AFMs depends on theresponse time of the detection mechanism (cantilever and readout), theactuator (scanner), the feedback electronics and the piezo driverelectronics. These components together form a feedback loop in which theperformance of the overall system is affected by phase delays andresonances in any of these components. As the resonance frequencies ofnew, small cantilevers reach frequencies around 280 kHz even for a softcantilever (0.006 N/m) in liquid, the new mechanical bandwidth is set bythe scanner, and by the mechanical superstructure. Therefore, to furtherimprove the capabilities of the AFM, special attention has to be givento the mechanical design of the scan and detection unit.

One of the main speed determining factors in an AFM system is thescanner, which is generally made with piezo crystals as the actuatingcomponents. In many commercially available systems piezo tubes are usedto generate the displacement in x, y and z directions. The active partof the scanner consists of a tube made out of piezoelectric materialsegmented into different sections. Tube scanners use the principle ofmechanical amplification to transform the small expansion of the piezosto a larger scan range. Scan ranges of commercial scanners can rangefrom 0.6 μm to 100 μm. This principle reduces the need for largecapacitance piezos and reduces the requirements on the amplifier.However, it also results in a weak mechanical structure and therefore alow mechanical resonance frequency (˜800 Hz). This is one of the primaryspeed limits of commercial tube scanners.

Another disadvantage of all kinds of piezos is their nonlinearity inoperation. Piezos exhibit a large position hysteresis, up to 30%, withrespect to the activating voltage. Piezos are also unstable in theirposition over time, changing its expansion even with a constantactuation voltage. These nonlinearities are a severe problem for the useof piezos as scanners for AEM as they distort the image, resulting inimage drift and making it hard to find the same spot on the sample afterzooming in. The hysteresis has to be accounted for either by amathematical model to correct the actuation voltage or by controllingthe actual piezo position in a closed loop feedback. Some commercialscanners model the piezo behavior, and changes in the actuating voltageare made by the controlling software. This approach has severaldisadvantages:

-   -   scanner parameters have to be measured for each individual        scanner, with up to thirty parameters needed to model the piezo        sufficiently;    -   the behavior of the piezo is dependant on the DC offset, scan        range and scan frequency; and    -   position creep is unaccounted for by the modeling.

For the user of the AFM this results in:

-   -   image warping (images are expanded in some directions and        compressed in others);    -   change of image center when zooming in or out; and    -   image drift    -   incorrectly measured sizes of the objects.

However, this approach does not need any sensors and all the modelingcan be done by the software and the digital signal processor.

The following references relate to the background of this invention: (1)C. F. Quate, et al., Atomic Force Microscope, Phys. Rev. Lett. 56 (1986)930; (2) D. Rugar, et al. Atomic Force Microscopy, Phys. Today 43 (10)(1990) 23; (3) Atomic resolution with the atomic force microscope onconductors and nonconductors, J. Vac. Sci. Technol. A 6 (1988) 271; (4)G. Schitter, et al., Robust 2DOF-control of a piezoelectric tube scannerfor high speed atomic force microscopy, Proceedings of the AmericanControl Conference, Denver, Colo., Jun. 4-6, 2003, pp. 3720; (5) D. A.Walters, et al., Short Cantilevers for Atomic Force Microscopy, Rev.Sci. Instrum. 67 (1996) 3583; (6) M. B. Viani, et al., Small cantileversfor force spectroscopy of single molecules, J. Appl. Phys. 86 (4) (1999)2258; (7) T. Ando, A high-speed atomic force microscope for studyingbiological macromolecules, Proc. Natl. Acad. Sci. USA 98 (22) (2001)12468; (8) Humphris, A D L, Hobbs, J K and Miles, M J, Ultrahigh-speedscanning near field optical microscopy capable of over 100 frames persecond, Apl. Phys. Let. 2003,83:6-8; (9) J. B. Thompson, et al.,Assessing the quality of scanning probe microscope designs,Nanotechnology 12 (2001) 394; (10) T. E. Schaffer, et al.,Characterization and optimization of the detection sensitivity of anatomic force microscope for small cantilevers, Journal of AppliedPhysics, (84), (No. 9) (2001), 4661; (11) T. E. Schaffer, et al., Anatomic force microscope using small cantilevers, SPIE—The InternationalSociety for Optical Engineering, (3009) (1997) 48; (12) T. E. Schaffer,et al, Studies of vibrating atomic force microscope cantilevers inliquid, Journal of Applied Physics, (80) (No. 7) (1996) 3622. See alsothe following U.S. patents: U.S. Pat. No. 5,825,020-Atomic forcemicroscope for generating a small incident beam spot, U.S. Pat. No.#RE034489-Atomic force microscope with optional replaceable fluid cell,and U.S. Pat. No. 4,800,274-High resolution atomic force microscope. Theforegoing publications and patents are all incorporated herein byreference.

SUMMARY OF THE INVENTION

The present invention overcomes the foregoing problems by providing anew type of scanner that avoids low resonance frequencies and accountsbetter for piezo nonlinearities. In accordance with one embodiment ofthe invention, we provide what we call a liner stack scanner. The linearstack scanner also uses piezo electric crystals as actuating components.However, these piezos are not single crystals but are made out ofinsulated layers of piezoelectric material that are electricallyconnected in parallel. Arranging the single crystals in parallelincreases the expansion range of the stack that is determined by thenumber of stacked single crystals. While each additional layer adds morecapacitance to the stack to increase the capacitive load on theamplifier, and the mechanical resonance frequency of the piezo stack islowered by each additional layer, coupled with the improved mechanicalperformance enabled by other embodiments of this invention, the linearstack scanner more than compensates for these effects.

In accordance with this invention, the x, y and z axes of the scannerare located perpendicular to each other and, are coupled to each other,but the piezos that actuate the axes are constrained in all directionsexcept for the direction of the desired actuation. The sample areadirectly responds to piezo actuation with mechanical deformation withinelastic limits, while maintaining x-y symmetry to enable image rotation.Speed performance is assured by rigidity in the actuation direction withhigh first order resonance frequencies, reducing mechanical oscillationswhile imaging. This is accomplished by cach of several embodiments ofthe invention. In essence, this aspect of the invention provides ascanning probe microscope comprising a probe, a housing, and at leasttwo actuators. Each actuator is coupled to the housing, and a support iscoupled to the housing. The support is also coupled to at least one ofthe actuators at a position spaced from the point at which the actuatoris coupled to the housing, for example, at an end opposite the endcoupled to the housing. The support constrains the motion of the firstactuator along a first axis while permitting translation along a secondaxis. The actuators are preferably piezoelectric but other types ofactuators can be used, for example, electostrictive, magnetostrictive,and/or electrostatic actuators, or even voice coils or electric motors.The actuators are preferably orthogonally arranged linearly stackedpiezos, more preferably in push-pull configuration. The support can takedifferent forms in different embodiments of the invention, as will bedescribed below in detail.

In a specific embodiment, the scanner has a support frame with x and yaxes, a centrally disposed member for supporting an object to be movedsuch as a sample for a probe, and a flexure. Linear piezo stacks arearranged along x and y axes, and flexure couplings formed of bladesprings are disposed between the piezos and the support frame onopposite sides of the support frame, arranged so that as there istranslation along a first of the x and y axes while blade springs alongthe second of the x and y axes bend to permit movement along the firstaxis. There are preferably two piezos for each axis in a push-pullarrangement, which can be referred to as “cross-conformed”, so that whenone piezo expands, the other one contracts, resulting in translation ofthe centrally disposed member.

In accordance with another embodiment of the invention, expansion of thepiezos is measured by strain gauges, for example metal foil straingauges. In this aspect, the invention comprises a probe, at least twoopposed actuators, and at least two strain gauges disposed to measurethe differential motion of the actuators. The strain gauges arepreferably ranged to compensate for ambient temperature changes, e.g.,in Wheatstone bridge fashion. Preferably, two strain gauges of identicaltype are disposed on each actuator to magnify the strain signal.

These and other aspects and advantages of the present invention willbecome better understood with regard to the following detaileddescription and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective schematic depiction of generalized components ofa scanner of this invention for a scanning probe microscope;

FIG. 2 is a perspective schematic depiction of generalized components ofa scanning probe microscope of this invention;

FIG. 3 is a perspective schematic depiction of a linear piezo stack usedin this invention, formed of insulated layers of flat piezo plates;

FIG. 4 schematically depicts the arrangement of linear piezo stacks fora cross-conformation push-pull scanner design in accordance with thisinvention;

FIG. 5 schematically depicts translation of the center of the push-pullconfiguration of linear piezo stacks defining the x axis of the scanner;

FIG. 6 schematically depicts a scanner with flexure coupling ofcross-conformed push-pull linear piezo stacks arranged along the x and yaxes of the scanner, and rigid in the z axis, in accordance with anembodiment of this invention, providing rigid, stiff movement along eachaxis effectively decoupled from forces normal to the respective x and yaxis;

FIG. 7 is a perspective, partially cross-sectional depiction of ascanner using the flexure coupling of FIG. 6;

FIG. 8 is a schematic top cross-sectional view of the scanner of FIG. 6depicting the flexure coupling in more detail than FIG. 4;

FIG. 9 depicts the first eigenfrequency of the flexure used in thescanner of FIG. 6, without side support, obtained by finite elementsimulation;

FIG. 10A depicts the first, third, and fifth eigenfrequencies of theflexure used in the scanner of FIG. 6, without side support;

FIG. 10B depicts the first, third, and fifth eigenfrequencies of theflexure used in the scanner of FIG. 6, with side support;

FIG. 11 is a perspective, partially cross-sectional depiction of ascanner in accordance with another embodiment of this invention. Abearing ball coupling is used having cross-conformed linear piezo stacksarranged along the x and y axes of the scanner, and which is rigid inthe z axis. It provides rigid, stiff movement along each axiseffectively decoupled from forces normal to the axis;

FIG. 12 is a schematic top view of the scanner of FIG. 11;

FIG. 13 shows plots of the frequency response of the bearing ballscanner of FIG. 11 with and without balance actuation from the lower zaxis piezo stack;

FIG. 14 is a perspective, partially cross-sectional depiction of ascanner in accordance with another embodiment of this invention, using acombination of bearing ball and flexure couplings wherein bearing ballscouple cross-conformed push-pull linear piezo stacks arranged along thex and y axes of the scanner, and a flexure couples cross-conformedpush-pull linear piezo stacks arranged along the z axis, providingisolation from x-y movement of the z axis and rigid, stiff movementalong each axis effectively decoupled from forces normal to the axis;

FIG. 15 is a schematic top view of the scanner of FIG. 14;

FIG. 16 schematically depicts the construction of a flexure coupling asused in the scanner of FIG. 14;

FIG. 17 depicts the first and second eigenfrequencies of a scanner withsimilar design as the one of FIG. 14

FIG. 18 shows plots of the step response of the top piezo, bottom,counter piezo, and balanced push-pull piezo combination of the bearingball scanner of FIG. 11;

FIG. 19A depicts an unbalanced bridge configuration using one straingauge, in a further embodiment of this invention; and

FIG. 19B depicts a temperature compensated unbalanced bridgeconfiguration using one strain gauge bridge using four strain gauges forhigher sensitivity, in a still further embodiment of this invention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 schematically depicts generalized components of the scanner 10for use in a scanning probe microscope of the invention. The scanner 10includes a housing 12, at least two actuators 14 and 16 (possiblytogether with respective opposing actuators 18 and 20), each coupled tothe housing 12, respectively at 24 and 26, and a support 22. The support22 is also coupled to the housing (not shown in FIG. 1) and to at leastone of the actuators at a position, e.g., at 28, spaced from the point24 at which the actuator is coupled to the housing 12. The support 22and its connections to actuators 14, 16, 18, and 20 are such that thesupport 22 constrains motion of each actuator along its axis whilepermitting translation normal to the axis. Strain gauge sensors 30, 32,34, and 36 are applied to respective actuators 14, 16, 18, and 20 toenable measurement of expansion or contraction of the actuators.

Referring to FIG. 2, generalized components of a scanning probemicroscope 11 of the invention are shown. The microscope 11 includes asample carrier 13 itself carried by a top linear piezo stack 60,described in more detail with respect to FIG. 4. An AFM head 15 isdisposed on the scanner housing 12 and carries a cantilever probe 17having its tip 19 in contact with a sample carried by the sample carrier13. The AFM head 15 includes a source (not shown) for a laser beam 21that reflects from the back of the cantilever probe 17 to a detector(not shown).

The invention contemplates a number of configurations, which will bedescribed in detail below.

The scanner 10 uses piezoelectric crystals (“piezos”) as actuatingcomponents. However, and referring to FIG. 3, these piezos are notsingle crystals, but are linear piezo stacks. Each stack 38 is formed oflayers of piezoelectric material 40 and electrically conducting plates42 separated by insulating layers 44 and electrically connected inparallel, e.g., by electrical connectors 46 and 48. Arranging the singlecrystals in parallel increases the expansion range of the stackdetermined only by the number of stacked single crystals. However, themechanical resonance frequency of the piezo stack is lowered by eachadditional layer. In addition, each additional layer does add morecapacitance to the stack, increasing the capacitive load on theamplifier.

Such piezos are commercially available, e.g., from NEC/Tokin(Part#AE0505D16). Various sizes are available with different achievabledisplacements, ranging from 2 μm to 16 μm and capacitances ranging from0.1 μF to 1.5 μF. The choice of piezo depends on the desired scan rangeand the needed frequency response.

A number of design parameters must be considered to obtain maximum speedperformance of the scanner:

-   -   (a) One of the most significant goals is to reduce mechanical        oscillations while imaging by providing a rigid design with high        first order resonance frequencies.    -   (b) The x, y and z axis of the scanner must be located        perpendicular to each other, but they have to be decoupled from        each other, and electrical and mechanical cross-coupling has to        be avoided.    -   (c) All mechanical joints have to be stiff in the actuation        direction to ensure direct response of the sample area to piezo        actuation.    -   (d) Mechanical deformation during operation has to be within        elastic limits, and mechanical stress levels during operation        have to be accounted for.    -   (e) The x and y axes should be symmetrical to enable image        rotation to be implemented.

The main objective for fast scanning is to achieve the strictproportionality between the actuation signal and the translation of thesample disc. Resonances of the scanner distort the proportionalresponse. Resonances in the x- and/or y-directions deform features inthe image. Resonances in z-direction result in a waved appearance ofotherwise flat surfaces, and for many applications are the most criticalto suppress. Thus, the aim of the design is to shift the firsteigen-resonance to higher frequencies. There are three ways to do this:reduce the moving mass, use rigid construction whenever possible, andavoid long mechanical levers, especially involving the sample holder.All three approaches have to be used and tradeoffs have to be madebetween them. As will be described in more detail below, to quantify theresonance behavior of the scanner, we tested the design for its firsteigenfrequencies using finite element analysis.

The scanner designs of this invention have a Cartesian conformationwhere we have separate actuators for each translation direction. Since apiezo's primary ability is to apply force when expanding but not whencontracting, in accordance with a preferred embodiment, we chose to havetwo piezos for each axis to allow movement in opposite directions.Referring to FIG. 4, a pair of opposed linear piezo stacks 50 and 52 aredisposed in push-pull fashion to define the x axis of the scanner, twolinear piezo stacks 54 and 56 are similarly disposed to define the yaxis, and another two linear piezo stacks 58 and 60 are similarlydisposed to define the z axis. Referring to FIG. 5, the two piezos ineach pair are electrically connected complimentarily, so that when onepiezo expands, the other one contracts, resulting in a translation of acenter support 62. Since the piezos that were used are unipolar, aDC-offset of half the voltage range (+75V) is applied to both piezosrepresenting the no signal position (or the neutral or center position,or the center of the scan range).

In order to expand this principle to the y-direction (perpendicular tothe image plane of FIG. 5), the coupling between each piezo and thecenter support 62 is critical. Ideally, this connection would be totallyrigid in the direction the piezo moves the sample, but totally flexiblein the other two directions. Several implementations of this couplingare described below, using either “flexure” coupling, bearing ballcoupling, or both.

Flexure Coupling

FIG. 6 schematically depicts a flexure coupling of cross-conformedpush-pull linear piezo stacks 64, 66 and 68, 70, respectively arrangedalong the x and y axes of the scanner, and rigid in the z axis. Thescanner has flexure couplings, respectively 72, 74, 76 and 78 betweenthe piezos and the flexing support frame 80. The left side (in thedrawing) x axis piezo 64 expands as the right side x axis piezo 66contracts, causing the blade springs (described below) of both y axisflexures 76 and 78 to bend, allowing movement of the x axis piezo stacks64, 66 to move the center member 82 of the scanner to the left.

The flexure couplings 72, 74, 76 and 78 provide rigid, stiff movementalong the respective x and y axes effectively decoupled from forcesnormal to the respective axes. FIGS. 7 and 8 depict, respectively inpartial cross-section and in schematic top view a scanner using theflexure coupling of FIG. 6. The piezos 64, 66, 68 and 70 laterally movethe whole center member 82 including counter balanced piezos 94 and 96for the z direction. The sample is mounted on the upper of the two zpiezos. The lower z axis piezo serves as a balance (which will bedescribed further below) for the upper z axis piezo 96. The centermember 82 is coupled to the piezos by respective flexures 72, 74, 76 and78, each formed of an array of blade springs. As described above, theflexures are rigid in their axial directions (parallel to the blades)but flexible perpendicular to the blades. Therefore, the center member82 can be moved in the x and y directions, but is rigid in thez-direction. Fine pitched screws 98, 100 and 102 serve to connect thescanner to the AFM head.

Referring to FIG. 9, the first eigenfrequency of the cross-configurationflexure used in the scanner of FIG. 6, without side support, wasobtained by finite element simulation. The analysis showed that thefirst eigenfrequency of the moving system is a transversal vibration ofthe piezos with the center moving with the biggest amplitude. This ishighly undesirable for an AFM scanner. In order to prevent thesevibrations, and in accordance with the invention, the flexing supportframe 80 is added around the center and attached to the body of thescanner. The frame is rigid in the z direction, but flexible in thedirections the x and y piezos push the sample. FIG. 10A depicts thefirst, third, and fifth eigenfrequencies of the flexure used in thescanner of FIG. 6, without side support obtained by finite elementanalysis. FIG. 10B depicts the first, third, and fifth eigenfrequenciesof the flexure used in the scanner of FIG. 6, with side support. Theresults are set forth in Table 1. With side supports, the mass anddimensions of the piezos no longer contribute to the vibrations of thescanner center so that larger piezos with more displacement can be usedwithout slowing the system down in directions perpendicular to theiractuation.

TABLE 1 Eigenfrequency f₀ Without side f₀ With side Number supports (Hz)supports (Hz) 1 5814 10590 2 11870 16949 3 12026 17009 4 12212 18761 512277 24131 6 12331 24959Bearing Ball Coupling

FIGS. 11 and 12 depict, respectively in partial cross-section and inschematic top view, a scanner using a bearing ball coupling ofcross-conformed linear piezo stacks 106, 108 and 110, 112, respectivelyarranged along the x and y axes of the scanner, and rigid in the z axis,providing rigid movement along each axis effectively decoupled fromforces normal to the axis. The center member 114 is mounted on the baseof the scanner with a 1-72 screw 116 that presses the center piece ontothree bearing balls, two of which, 118 and 120, being shown in FIG. 11.The top and bottom balanced z-piezos 122 and 124 are mounted on thecenter piece. The x and y piezos, respectively 106, 108 and 110, 112,move the center member 114 by pushing on bearing balls that in turn pushon the center piece. This approach is fundamentally different from theflexure design shown in FIGS. 6-8. In the flexure scanner, theconnections between the x and y piezos and the center member providesupport to the center member in the x- and y-directions, as well as inthe z-direction. In the bearing ball design, the z support is given bythe three bearing balls on the bottom. This results in a much higherresonance frequency in the important z-direction (e.g., simulated 27kHz) so that the center section is better supported, therefore improvingperformance.

The x and y axis piezos in this embodiment are also supported at theirinner ends by a flexing frame 126 that couples them to the base 128.This increases the resonance frequency of the assembly considerably, asdescribed with respect to FIGS. 6-8. The moving mass in this assembly ismainly determined by the mass and size of the two z-piezos. A tradeoffhas to be made here between scan-range and resonance frequency. Thefrequency spectrum of this scanner is shown in FIG. 13, showing aresonance peak at around 6 kHz; the effect of the resonance is very wellcompensated by the counter piezo.

Combined Flexure and Bearing Ball Couplings

In a further embodiment, in order to further reduce the moving mass ofthe scanner, a combination of the bearing ball support for the x, ydirections and a flexure for the support in z direction is implemented.FIGS. 14 and 15 depict, respectively in partial cross-section and inschematic top cross-sectional view, a scanner in accordance with anotherembodiment of this invention, using a combination of bearing ball andflexure couplings wherein bearing balls 130 couple cross-conformedlinear piezo stacks 132, 134 and 136, 138 arranged respectively alongthe x and y axes of the scanner, and a flexure 140 couples balancedpiezo stack pair 142 and 144 arranged along the z axis, providingisolation from x-y movement of the z axis and rigid, stiff movementalong each axis effectively decoupled from forces normal to the axis.

FIG. 16 schematically depicts the construction of a flexure coupling asused in the scanner of FIGS. 14 and 15. In essence, the flexure is anarray of rods 146, each of which is rigid along its axis while beingcompliant in the translational directions normal to its axis. Along itsaxis, a rod has a spring constant determined by its length, itscross-section, and its elastic modulus in compression. Laterally, a rodhas the spring constant of a bending beam. The spring constant in alltranslational directions scales linearly with the number of rods, theratio between axial and lateral spring constants being conserved.

As shown in FIG. 16, the flexure can be constructed by machining aseries of parallel cuts 148 into a block 150 of suitable material, e.g.,beryllium-copper, aluminum, stainless steel, etc., leaving a series ofblades 152 of the material attached on one side of a base 154. The pieceis then rotated and a second series of cuts 156 is machinedperpendicular to the first set, leaving the array of rods 146. Thecutting is virtually frictionless by using wire electron dischargemachining (wire-EDM).

The main difference between the embodiment of FIGS. 14 and 15 comparedto the previous embodiments is that the piezos for the z direction arenot being translated in x and y direction. The balanced z piezos arestationarily mounted on the base of the scanner, supported on one sideby the base and coupled on the other side to a flexure. When the z-piezoexpands, it moves the 2D-flexure plus the center piece up and down.

The x, y support by bearing balls had proven very effective, and wastherefore only slightly modified from the previous version. FIG. 17shows the first two eigenfrequencies of a scanner of this design type.Table 2 lists the first six eigenfrequencies of this scanner.

TABLE 2 Eigenfrequency Number Frequency (Hz) 1 44048 2 45296 3 45384 448710 5 55839 6 66667

In the embodiments of this invention, z actuation is implemented using apair of piezo stacks in “balanced configuration”. The two piezos areelectrically connected in parallel, in order to minimize the impulseapplied onto the center piece. When the upper piezo expands, itaccelerates the sample. The impulse on the sample also gets transmittedto the center member of the scanner, thereby exciting the z-resonance ofthe scanner. To minimize this, a second piezo is mounted underneath theprimary z-piezo. It expands and contracts in phase with the primarypiezo. The counter piezo exhibits as much impulse on the center memberas the primary piezo, ideally resulting in no effective impulse on thescanner's center piece. FIG. 13 shows the frequency spectrum of thebearing ball scanner with and without the counter piezo activated. Onecan see that the resonance at 6 kHz is reduced considerably in magnitudewhen using the counter balance piezo. For imaging, the oscillations inthe step-response result in ripples behind edges in the image. Whenusing the balanced actuation, this effect is reduced considerably. Thisbehavior is also shown in the step response of the scanner, shown inFIG. 18

Strain Gauge Sensors

The expansion of the piezos is measured by metal foil strain gauges.When stress is applied to the strain gauges, their resistance increases.In order to measure this small effect, strain gauges are normally oneactive part in a resistor bridge as shown in FIG. 19A. Strain gaugeshave the disadvantage of being temperature sensitive. When thetemperature of the strain gauge rises it changes its resistance. Thiswould be interpreted as a change in expansion of the piezo. Standardstrain gauge procedures take care of this problem by replacing one ormore of the resistors by dummy strain gauges that do not measure strainbut eliminate the temperature influence in the bridge circuit. However,the signal change is not very large for expansions of the piezos of theorder of μm. The output signal of the bridge can be calculated for achange of ΔR in resistance of the strain-gauge due to a change instrain.

$U_{Sig} = {U_{i\; n}\left( {\frac{R_{2}}{R_{1} + R_{2}} - \frac{R_{SG}}{R_{3} + R_{SG}}} \right)}$${\Delta\; U_{Sig}} = {U_{i\; n}\left( {\frac{R_{SG}}{R_{3} + R_{SG}} - \frac{R_{{SG}_{1}} + {\Delta\; R_{SG}}}{R_{3} + \left( {R_{SG} + {\Delta\; R_{SG}}} \right)}} \right)}$assuming  Δ R_(SG)<< R_(SG)${\Delta\; U_{Sig}} = {U_{i\; n}\left( \frac{{- \Delta}\; R_{SG}}{R_{3} + R_{SG}} \right)}$for:  R = R_(SG) = R₃${\Delta\; U_{Sig}} = {U_{i\; n}\left( \frac{{- \Delta}\; R}{2R} \right)}$

In the foregoing equations, U_(in) is the voltage applied to the inputterminals of the strain gauge bridge, U_(Sig) is the voltage between theoutput terminals of the strain gauge bridge and R_(x) is the resistanceof the particular resistors

In the linear stack scanner, a different full bridge compensation wasused. Two identical strain gauges were glued to each piezo stack inorder to magnify the strain gauge signal. The strain gauges for the twopiezo stacks for each direction are connected as shown in FIG. 19B. Thestrain gauges S_(G1) and S_(G1) are glued onto one piezo and S_(G2) andS_(G2) onto the second piezo for each direction. When piezo 1 expands,piezo 2 contracts, the strain gauges S_(G1) and S_(G1) get higherresistance and the strain gauges S_(G2) and S_(G2) get lower resistance.This approach has several advantages:

-   -   as long as the temperature of the two piezos is identical, an        absolute temperature change does not change the output of the        bridge,    -   the output of the full bridge signal gets doubled, this        increases the sensitivity and improves the signal to noise ratio        and    -   the full bridge is attached rigidly to the piezos        The output signal from the strain gauge bridge is then

$U_{Sig} = {U_{i\; n}\left( {\frac{\overset{\_}{R_{{SG}_{2}}}}{\overset{\_}{R_{{SG}_{1}}} + \overset{\_}{R_{{SG}_{2}}}} - \frac{R_{{SG}_{1}}}{R_{{SG}_{2}} + R_{{SG}_{1}}}} \right)}$for  Δ R<< R_(SG₁), R_(SG₂)${\Delta\; U_{Sig}} = {U_{i\; n}\left( {\frac{\overset{\_}{R_{{SG}_{2}}} + {\Delta\; R}}{\overset{\_}{R_{{SG}_{1}}} + \overset{\_}{R_{{SG}_{2}}}} - \frac{R_{{SG}_{1}} - {\Delta\; R}}{R_{{SG}_{2}} + R_{{SG}_{1}}}} \right)}$${{for}\text{:}\mspace{14mu} R} = {R_{{SG}_{1}} = {R_{{SG}_{2}} = {\overset{\_}{R_{{SG}_{1}}} = \overset{\_}{R_{{SG}_{2}}}}}}$${\Delta\; U_{Sig}} = \frac{\Delta\; R}{R}$A constant voltage (10V) is applied to the U_(in) terminals of the fullbridge. This results in an output signal of the strain gauges of 20 mV.In order to minimize noise, amplification of this signal (located closeto the bridge) is needed. Amplification is done by an instrumentationamplifier. Because the outputs of the bridge are close to 5V DC and theAC component of the signal is small, a high common mode rejection isneeded (at least 110 dB).Triangular Scanning vs. Sine Wave Scanning

In conventional Atomic Force Microscopes a triangular wave is used toscan the sample with respect to the cantilever tip. Height anddeflection information can then be linearly plotted over time torepresent position on the surface. For fast imaging this approach isvery unfavorable, because the acceleration forces on the scanner at theturn around points are very high. Higher order resonances are beingexcited since the triangular wave is composed of higher order Fouriercomponents. This very much distorts the image. For fast imaging it isbetter to scan the sample with a sine wave and account for thenonlinearity when plotting the image.

1. A scanning probe microscope, comprising: a probe; a housing; at leasttwo actuators, each coupled to the housing; and a flexure coupled to thehousing and to at least a first of the actuators at a position spacedfrom the point at which the actuator is coupled to the housing.
 2. Thescanning probe microscope of claim 1 in which the actuators are arrangedin opposed push-pull configuration.
 3. The scanning probe microscope ofclaim 1 in which the actuators are orthogonally arranged linear piezostacks.
 4. The scanning probe microscope of claim 1 in which the flexureis coupled to at least one actuator at an end opposite the end coupledto the housing.
 5. The scanning probe microscope of claim 1 wherein theflexure constrains the motion of the first actuator along a first axiswhile permitting translation along a second axis.
 6. A scanning probemicroscope, comprising: a probe; a scanner for the microscope having asupport frame with x and y axes, and a member for supporting a samplefor the probe, the scanner comprising a flexure and flexure coupledcross-conformed actuators arranged along said x and y axes.
 7. Thescanning probe microscope of claim 6 in which the flexure couplings arebetween the actuators and the support frame.
 8. The scanning probe ofclaim 6 in which actuators are arranged on opposite sides of the supportframe in push-pull configuration.
 9. The scanning probe microscope ofclaim 6 in which said sample supporting member is in the center of thesupport frame.
 10. The scanning probe microscope of claim 6 in which theflexures are formed of blade springs.
 11. The scanning probe microscopeof claim 10 in which the blade springs are arranged so that as there isactuators expansion along a first of said x and y axes, the bladesprings along the second of the x and y axes bend to permit movementalong said first axis.
 12. The scanning probe microscope of claim 6 inwhich the actuators are orthogonally arranged piezos.
 13. The scanningprobe microscope of claim 12 in which the piezos are linear piezostacks.
 14. The scanning probe microscope of claim 6 includingcross-conformed actuators arranged along the z axis.
 15. The scanningprobe microscope of claim 14 in which the actuators are orthogonallyarranged piezos.
 16. The scanning probe microscope of claim 15 in whichthe piezos are linear piezo stacks.
 17. A scanning probe microscope,comprising: a probe; a scanner for the microscope having a support framewith x and y axes and a centrally disposed member for supporting asample for the probe, the scanner comprising a flexure, cross-conformedpush-pull linear piezo stacks arranged along said x and y axes, andflexure couplings formed of blade springs between the piezos and thesupport frame on opposite sides of the support frame, arranged so thatas there is piezo expansion along a first of said x and y axes, theblade springs along the second of the x and y axes bend to permitmovement along said first axis.
 18. A scanner, comprising: a supportframe with x and y axes and a member for supporting an object to bemoved, the scanner comprising a flexure and flexure coupledcross-conformed piezos arranged along x and y axes.
 19. The scanner ofclaim 18 in which the flexure couplings are between the piezos and thesupport frame.
 20. The scanner of claim 18 in which piezos are arrangedon opposite sides of the support frame in push-pull configuration. 21.The scanner of claim 18 in which the object support member is in thecenter of the support frame.
 22. The scanner of claim 18 in which theflexures are formed of blade springs.
 23. The scanner of claim 22 inwhich the blade springs are arranged so that as there is piezo expansionalong a first of said x and y axes, the blade springs along the secondof the x and y axes bends to permit movement along said first axis. 24.The scanner of claim 18 in which the piezos are linear piezo stacks. 25.A scanner, comprising: a support frame with x and y axes and a centrallydisposed member for supporting an object to be moved, the scannercomprising a flexure, cross-conformed push-pull linear piezo stacksarranged along said x and y axes, and flexure couplings formed of bladesprings between the piezos and the support frame on opposite sides ofthe support frame, arranged so that as there is piezo expansion along afirst of said x and y axes, the blade springs along the second of the xand y axes bend to permit movement along said first axis.